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The coupled effects of sample size and grain size and the plastic deformation mechanisms of polycrystalline Al nanowires were investigated by molecular dynamics. With the number of grains across the diameter increasing from one to four, the 5nm grain size nanowires showed a “smaller is stronger” effect, the 10nm grained nanowires did not show any significant size effect, while the 20nm grained nanowires showed a “smaller is weaker” effect. Different size effects are induced by competition between surface-mediated and grain boundary-mediated deformations. [Copyright &y& Elsevier]

The compressive behavior of hollow micropillars is modeled by three-dimensional discrete dislocation dynamics (3D-DDD). Computational results show that wall thickness is the principal geometrical parameter governing the compressive strength of these micropillars, while inner or outer diameter has a weak influence. This is because the plastic behavior is dominated by the single-arm dislocation sources with statistical lengths determined by the wall thickness. The single-arm source model is further extended to quantitatively describe this thickness effect, showing good agreement with the present 3D-DDD results. [Copyright &y& Elsevier]

Abstract: 2D discrete dislocation dynamic modeling of compressed micro-pillars attached on a huge base is executed to study the size-dependent microplastic behavior of micro-pillars and the corresponding size effect. In addition to the conventional dimensional parameters of the micro-pillar such as the micro-pillar size and the height-to-width ratio, the micro-pillar taper angle and the dislocation slip plane orientation angle in the micro-pillar are also considered to address the size effect and its rich underlying mechanism. Computational results show that there are at least two operating mechanisms responsible for the plastic behavior of micro-pillars. One is associated with the dislocation free slip-out from the micro-pillar sidewall; the other is related to the dislocation pile-up at the base and the top end of the pillar. The overall mechanism governing the size effect of the micro-pillar rests with multi-factors, including the micro-pillar size, the height-to-width ratio, the micro-pillar taper and the slip plane orientation angle; however, whether the “free slip band” exists or not is the most important denotation. The well-known Schmid law still validates in the slender micro-pillars due to existence of the free slip band, whereas it may fail in the podgier micro-pillars due to absence of the free slip band; as a result, a complicated even “reverse” size effect appears. [Copyright &y& Elsevier]

Abstract: A two-dimensional discrete dislocation dynamics (DDD) technology by Giessen and Needleman (1995), which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocation-penetrable grain boundaries (GBs) on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation. [Copyright &y& Elsevier]

Abstract: Nanoindentation has been extensively used to measure the mechanical behavior of materials at the micro- and nanoscale. However, the material response of nano/microindentation and its intrinsic mechanisms are very complicated, especially when considering heterogeneous polycrystalline materials. In this contribution, nanoindentation in polycrystals, performed with a circular indenter, is studied by numerical modeling based on the two-dimensional discrete dislocation plasticity of Van der Giessen and Needleman [Van der Giessen E, Needleman A. Model Simul Mater Sci Eng 1995;3:689]. The dependence of indentation hardness is investigated with respect to four typical characteristic dimensions: indenter radius, grain size, indentation depth, and the distance between the grain boundary and the indenter. Results show that these characteristic dimensions have considerable influence on the nanoindentation hardness. Further investigation shows that their influence takes effect mainly in two ways, i.e. via strain hardening and the indentation size effect. Although both effects are size dependent, their underlying mechanisms are clearly different. For the present polycrystal case, the strain hardening effect is mainly associated with the constraints of grain boundaries and dislocation obstacles to the dislocation glide, while the indentation size effect is related to the average strain gradient beneath the circular indenter. [Copyright &y& Elsevier]

Abstract: The cyclic plastic response of a single crystalline thin beam subject to combined cyclic tension and bending is analyzed using two-dimensional discrete dislocation plasticity. In this contribution, special attention is paid to the difference in the inherent mechanism of the size effect for different cyclic loads. Results show that the cyclic plastic response has a strong size effect for both cyclic pure tension–compression and pure bending. However, the inherent mechanisms are different. The dislocation starvation mechanism dominates the cyclic tension–compression while the geometrically necessary dislocation dominates the cyclic pure bending. When the combined cyclic tension and bending are applied to the thin beam, the cyclic moment–rotation response shows strong size effect while the stress–strain response shows weak or even no size effect. In addition, it is also found that the cyclic loading paths have considerable influences on the shape of the cyclic stress–strain loops. [Copyright &y& Elsevier]

Abstract: In the present paper, an infinite face-centered cubic single crystal containing an isolated cylindrical micron-sized void, which is subjected to proportional and monotonically uniform equal biaxial tension loading, is adopted to study the scale-dependent void growth and its intrinsic mechanism by employing a two-dimensional planar discrete dislocation dynamic framework. First, a typical dislocation distribution near the microvoid is presented and the void growth mechanism is revealed by dislocation shear loop expansion for each of three typical fcc slip systems. The effect of size on void growth is then investigated. The general conclusion that voids at the micron or submicron scale are less susceptible to growth than larger ones is drawn. Another result, which cannot be deduced from the continuum theories, is also achieved: at the micron or submicron scale, larger voids grow smoothly with remote strain, while smaller voids usually grow in a “leapfrog” manner. Specifically, when the void is even smaller, it grows in an approximately linear-elastic manner since only few dislocations are present around the void. Further analyses indicate that these size effects are closely related to the dislocation density on the void surface and the dislocation mobility around the void. Finally, the influences of the dislocation sources/obstacles density and their random distribution in materials on the void growth are studied briefly. Results show that there exists remarkable scatter in the microvoid growth due to random distribution of the dislocation sources or obstacles, especially for voids at the submicron scale. These results are helpful for us in understanding the size-dependent damage mechanism at the micron or submicron scale. [Copyright &y& Elsevier]

Abstract: The present paper extends the Gurson and GLD models [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Mech. Phys. Solids 99, 2–15; Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 116, 290–297] to involve the coupled effects of void size and void shape on the macroscopic yield behavior of non-linear porous materials and on the void growth. A spheroidal representative volume element (RVE) under a remote axisymmetric homogenous strain boundary condition is carefully analyzed. A wide range of void aspect ratios covering the oblate spheroidal, spherical and prolate spheroidal void are taken into account to reflect the shape effect. The size effect is captured by the Fleck–Hutchinson phenomenological strain gradient plasticity theory [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, pp. 295–361]. A new size-dependent damage model like the Gurson and GLD models is developed based on the traditional minimum plasticity potential principle. Consequently, the coupled effects of void size and void shape on yield behavior of porous materials and void growth are discussed in detail. The results indicate that the void shape effect on the yield behavior of porous materials and on the void growth can be modified dramatically by the void size effect and vice versa. The applied stress triaxiality plays an important role in these coupled effects. Moreover, there exists a cut-off void radius r c, which depends only on the intrinsic length l 1 associated with the stretch strain gradient. Voids of effective radius smaller than the critical radius r c are less susceptible to grow. These findings are helpful to our further understanding to some impenetrable micrographs of the ductile fracture surfaces. [Copyright &y& Elsevier]

Abstract: Separation of the particle–matrix interface and breakage of the second-phase particle are two main void nucleation mechanisms, which are directly associated with the stress concentration factors (SCFs) at the interface and within the particle, respectively. This work investigates the coupled effects of particle size and particle shape on these stress concentrations by solving an infinite solid containing an oblate spheroidal particle under remote stress boundary condition. The phenomenological strain plasticity theory by Fleck–Hutchinson [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33. Academic Press, New York, pp. 295–361] is adopted to capture the size effect, various particle aspect ratios are considered to depict the particle shape effect and an interfacial energy concept is introduced to settle the double-traction equilibrium problem at the matrix–particle interface. By using a Ritz procedure, solutions about the stress concentrations are numerically achieved and three main results are found. First, the interfacial normal stress near the particle pole, the interfacial shear stress and the particle opening stress are dramatically elevated and their distributions are significantly modified by decrease in the particle size. Second, this particle size effect is influenced by the remote effective strain, remote stress triaxiality and the interfacial energy to different extent. Finally, the particle shape effect is coupled with this particle size effect, and the more oblate the particle is, the more significant the size effect on SCF elevation is. These findings are helpful for us to understand deeply the void nucleation mechanism at the micron scale. [Copyright &y& Elsevier]

Abstract: There generally exist two void nucleation mechanisms in materials, i.e. the breakage of hard second-phase particle and the separation of particle–matrix interface. The role of particle shape in governing the void nucleation mechanism has already been investigated carefully in the literatures. In this study, the coupled effects of particle size and shape on the void nucleation mechanisms, which have not yet been carefully addressed, have been paid to special attention. To this end, a wide range of particle aspect ratios (but limited to the prolate spheroidal particle) is considered to reflect the shape effect; and the size effect is captured by the Fleck–Hutchinson phenomenological strain plasticity constitutive theory (Advance in Applied Mechanics, vol. 33, Academic Press, New York, 1997, p. 295). Detailed theoretical analyses and computations on an infinite block containing an isolated elastic prolate spheroidal particle are carried out to light the features of stress concentrations and their distributions at the matrix–particle interface and within the particle. Some results different from the scale-independent case are obtained as: (1) the maximum stress concentration factor (SCF) at the particle–matrix interface is dramatically increased by the size effect especially for the slender particle. This is likely to trigger the void nucleation at the matrix–particle interface by cleavage or atomic separation. (2) At a given overall effective strain, the particle size effect significantly elevates the stress level at the matrix–particle interface. This means that the size effect is likely to advance the interface separation at a smaller overall strain. (3) For scale-independent cases, the elongated particle fracture usually takes place before the interface debonding occurs. For scale-dependent cases, although the SCF within the particle is also accentuated by the particle size effect, the SCF at the interface rises at a much faster rate. It indicates that the probability of void nucleation by the interface separation would increase. [Copyright &y& Elsevier]

• The size-dependent microvoid growth in heterogeneous polycrystals is studied by local/non-local (MSG) CPFEM. • The first kind of void-growth size effect by void-grain size ratio is investigated. • The second kind of void-growth size effect by absolute microvoid size is studied. • Stress triaxiality T has a significant influence on the void-growth size effect, while Lode parameter L exhibits a negligible effect. • The void-growth size effect in polycrystalline environments should be understood from a statistical point of view. Microvoid growth involves a strong size effect, i.e., smaller microvoid presents a lower growth rate. In polycrystalline materials, the size ratio between microvoids and grains may also affect microvoid growth behavior. However, most previous studies treated material matrix surrounding microvoids as homogeneous. It turned out that such treatment cannot effectively depict the influence of the abovementioned void-grain size ratio on damage evolution. In the present study, both classical local and non-local strain-gradient crystal plasticity finite element simulations are performed to study size-dependent microvoid growth in heterogeneous polycrystals. The results indicate that both void-grain size ratio and absolute microvoid size influence microvoid growth significantly, referred to as first (induced by grain-scale heterogeneous deformation) and second kinds of (induced by plastic strain gradient) size effects, respectively. Besides, macroscopic stress triaxiality T has a significant influence on the size effect of microvoid growth, while Lode parameter L exhibits a negligible effect. Due to random grain-orientation distribution and grain-geometric characteristic, a smaller microvoid within polycrystalline environments may even grow faster than a larger one, implying that the size effect of microvoid growth should be understood from a statistical point of view in polycrystalline environments. The present study provides a fundamental understanding on the intrinsic mechanism of the size-dependent microvoid growth in heterogeneous polycrystals. [Display omitted] [ABSTRACT FROM AUTHOR]

The interaction between a type-I blunt crack and a near-tip void were modeled by the two-dimensional discrete dislocation dynamics (2-D DDD), with special emphasis on the void growth, crack-tip deformation and their size effect. Different from the classical crystal plasticity-based FE modeling, the present 2-D DDD modeling clearly indicates that, even for the type-I opening crack, the horizontal slip bands connecting the crack tip and the void surface are easily formed, especially when the ligament between the crack-tip and void surface is not too long. Besides the horizontal slip bands, some asymmetric slip bands which are at an oblique angle to the horizontal x -axis can also be formed and intersect with the micro-void. On two coupled parallel slip bands, some oppositely signed dislocations, which can be regarded as equivalent prismatic dislocation loops, glide toward the void/crack-tip surface and thus drive the void growth and the crack tip further blunting. In addition, the size effect by ligament length and void radius on void growth and crack-void interaction has also been investigated carefully. It was found that the size effect is closely related to the formation of horizontal shear slip bands. There exists a critical void radius, under which the near-tip void tends to change into a flat shape and its area decreases gradually with increasing the applied stress intensity factor (SIF) K . These results might be helpful for a better understanding of the fracture and damage mechanisms in the crack-tip process zone. [ABSTRACT FROM AUTHOR]

Abstract: The indentation response of aluminum–matrix SiC particle-reinforced metal matrix composites (PR-MMCs) impressed by a circular indenter has been numerically analyzed under the two-dimensional discrete dislocation plasticity combined with the ANSYS® finite element software. Dependence of the nominal hardness HN on multiple factors, including the particle size, the particle area fraction, the matrix thickness between the indenter and the particle, the indentation location as well as the particle shape, is addressed in detail. Herein, we show that the nano-indentation response of the PR-MMCs is strongly associated with the particle area fraction of PR-MMCs as well as the blocking of dislocation free gliding within the matrix. At a high particle area fraction of 25%, HN increases with the decrease of the particle size due to the increasing blocking effect of particles on the dislocation gliding. However, at a low particle area fraction of 9%, a reverse dependence of HN could be observed, which is attributed to the formation of long free-slip bands in the matrix. [Copyright &y& Elsevier]